Answer and Step-by-step explanation:
[tex]Greetings![/tex]
[tex]Let's~answer~ your ~question![/tex]
[tex]\underline{\bold{It~is~given~that:}}[/tex]
[tex]The ~radius~ of ~the ~round ~path: r = 18~ feet[/tex]
[tex]The~ length ~of ~the ~distance ~cover ~by ~wheel : l = 38 ~feet[/tex]
[tex]Let ~The ~angle~ of ~rotation :\phi[/tex]
[tex]\underline{\bold{Now, ~According ~to~ question:}}[/tex]
[tex]\therefore length~ of ~the ~arc~ of ~a ~circle ~subtending ~an ~angle~ at~ center = \phi[/tex]
[tex]length ~of ~the ~distance ~cover ~by ~wheel =\boxed{~~ \pi \times radius \times~\frac{\phi}{180\degree^{o} }~ ~}[/tex]
[tex]Since ~180^{o} \ = \pi ~radian[/tex]
[tex]So,~ length~ of~ the ~distance~ cover~ by ~wheel~ \boxed{~~180^{o} \times raius \times \frac{\phi}{180^{o}} ~~}[/tex]
[tex]\underline{\bold{i.e:}}[/tex]
[tex]l=r \times \phi[/tex]
[tex]Or, \phi=\frac{38~feet}{18~feet}[/tex]
[tex]Or,~\phi =2.11^{o}[/tex]
[tex]\bold{Thus,~the~angle~of~rotation~is=2.11^{o}}[/tex]
